One notable feature of the Depoe Bay basalts is the way the pillows are interbedded with sediments. In some spots, such as this one, the pillows appear to be completely surrounded by, and supported in, the sandstone. My best guess would be that discrete pillows formed on the sea floor, then foundered into the underlying unconsolidated sediment. Alternatively, they might be invasive- that is the pillows may have formed by intrusion of lava into the sediment below- but that seems less likely, to me at least, to form such nice, round, and normal-looking pillows. It seems quite unlikely that this was a simultaneous deposition of such quantities of both lava and sediment.
This area is not very accessible; we're standing on a sidewalk about 15 or 20 feet above the outcrop, with a vertical wall dropping down to the exposure. But it might be possible to come in from the south, near the passage into the harbor, and walk up to get a closer look at the nature of this deposit. Both of my preferred explanations would require soft sediment deformation, evidence of which might or might not be visible with a closer look. I'd also want to take a closer look at the composition of the finer material, with an eye toward sorting out terrigenous clastics from basaltic breccia fragments, and also to look for evidence of hydrothermal alteration. The latter might support the idea of invasive pillows. Until then, though, the geology from a distance isn't bad.